Analytical Solution to a Voltage Driven Piezoelectric Element
The performance analysis of piezoelectric crystals or ceramic elements as employed in ultrasonic transducers is typically carried out by electric equivalent circuit models such as KLM  or, more recently, by numerical analysis techniques . Piezoelectric finite element formulations, which allow for flexible domain discretization, have emerged as powerful simulation tools for complex sensor configurations. Unfortunately, verification of these numerical programs by analytical theories is difficult, even for the simple one-dimensional single crystal resonator. Indeed, there is a particular need for a transient transducer model since practical NDE requirements often dictate a time domain treatment of the ultrasonic probe response driven by an applied voltage.
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